<p>Accurate prediction of liquid-vapor interface configurations is mission-critical for autonomous on-orbit propellant management, particularly during microgravity refueling operations where precise fluid control dictates mission success. In such environments, the systematic and rigorous evaluation of hydrostatic interfaces plays a vital role in ensuring optimal performance during liquid management and spacecraft attitude control. These fluid interfaces are primarily governed by residual gravitational effects, contact angles, and the geometric configurations of the containers. This paper investigates the characteristics of liquid-vapor interfaces within axisymmetric containers through a combination of theoretical analysis and numerical simulations. The dimensionless governing equations for hydrostatic surfaces in spherical coordinates are derived theoretically, based on the variational principle and the virtual work principle. A novel algorithm has been developed to compute liquid-vapor interface configurations in axisymmetric containers including ellipsoidal and Cassini tanks. The algorithm is validated by theoretical analysis and comparisons of numerical simulations and experimental data. Meanwhile, the impacts of various parameters on the liquid-vapor interface configurations are further analyzed in detail. Notably, the proposed method demonstrates significantly enhanced computational efficiency compared to conventional approaches. Furthermore, the algorithm can adaptively adjust its input parameters to predict hydrostatic interfaces under varying conditions. This methodology establishes a reliable foundation for real-time analysis of sloshing dynamics and liquid reorientation, thereby enabling autonomous decision-making during critical on-orbit refueling servicing phases.</p>